1. Field of the Invention
This invention relates to rate sensors for sensing applied rate about two axes.
2. Discussion of Prior Art
The use of ring shaped resonators in two axis Coriolis rate sensors is well known. Examples of such devices and their mode of operation are described in GB 2335273 and GB 2318184.
The devices described in GB 2335273 make use of a single out of plane cos Nθ vibration mode (where N is the mode order) in combination with a degenerate pair of in plane sin(N±1)θ/cos(N±1)θ vibrations modes. The out of plane cos Nθ mode acts as the primary carrier mode which is typically maintained at a fixed vibration amplitude. Under rotation around the appropriate axes, Coriolis forces are induced which couple energy into the in plane sin(N±1)θ/cos(N±1)θ modes. The amplitude of the induced in plane response mode motion is directly proportional to the applied rotation rate.
The two axis rate sensor designs described in GB 2318184 make use of a single in plane cos Nθ vibration mode in combination with a degenerate pair of out of plane sin(N±1)θ/cos(N±1)θ vibration modes. The in plane cos Nθ mode acts as the primary carrier mode which is typically maintained at a fixed vibration amplitude. Under rotation around the appropriate axes, Coriolis forces are induced which couple energy into the out of plane sin(N±1)θ/cos(N±1)θ modes. The amplitude of the induced out of plane response mode motion is directly proportional to the applied rotation rate.
In all of the example devices the carrier and the two response mode frequencies are required to be nominally identical. With these frequencies accurately matched the amplitude of the response mode vibration is amplified by the mechanical quality factor, Q, of the structure. This inevitably makes the construction tolerances more stringent. In practice, it may be necessary to fine-tune the balance of the vibrating structure or resonator by adding or removing material at appropriate points. This adjusts the stiffness of mass parameters for the modes and thus differentially shifts the mode frequencies. Where these frequencies are not matched the Q amplification does not occur and the pick-offs must be made sufficiently sensitive to provide adequate gyroscope performance. For a perfect unsupported ring structure fabricated from radically isotropic material, any given pair of in or out of plane sin Nθ/cos Nθ modes will have identical frequencies for any value of N. This degeneracy may be perturbed due to the requirement for the leg structures which support the ring. These have the effect of point spring masses acting at the point of attachment to the ring which will alter the modal mass and stiffness. In the designs described above, the number and spacing of the support legs is such that the symmetry of the response mode pair is maintained. The stated condition to achieve this requirement is that the number of legs, L, is given by:L=4×Nwhere N is the response mode order. These legs are set at an angular separation of 90°/N. The resonator dimensions are set in order to match the carrier mode frequency to that of the response mode pair. Matching of the frequency of the second complementary mode of the carrier mode pair is not required.
Inducing a deliberate, large frequency split between the cos Nθ carrier mode and its complementary sin Nθ mode is desirable in that it prevents any undesirable interaction between these modes and fixes the orientation of the carrier mode on the ring. Fixing the mode orientation enables the carrier mode drive and pick-off to be precisely aligned in their optimum angular location to excite and detect the carrier mode vibration. GB-A-2335273 and GB-A-2318184 do not provide any teaching on how to achieve a large frequency split with know fixed mode orientations for the Cos Nθ carrier mode and its complementary sin Nθ mode.
This requirement for the number of legs indicates that, for a sin 2θ/cos θ mode pair, eight support legs will be needed, twelve for a sin 3θ/cos 3θ mode pair, sixteen for a sin 4θ/cos 4θ mode pair etc. These leg structures are required to suspend the ring but must allow it to vibrate in an essentially undamped oscillation in response to applied drive forces and Coriolis forces induced as a result of rotation of the structure. A leg design suitable for suspending dual axis rate sensors using planar ring structures in shown in FIG. 1. This design has twelve legs and would be an appropriate arrangement for use with sensors using sin 3θ/cos 3θ mode pairs according to the prior art (number of legs=4XN, where N=3). These support legs have a linear part 9′ attached to the inner circumference of the ring 5 extending radially towards the common axis 8, a second linear part 9″ extending from a central boss 20 on an insulating substrate 10 away from the central axis 8 and radially displaced from the first part. The first and second part are connected by an arcuate section 9′″ concentric with the ring 5. The three parts will be integrally formed. It will be understood by those skilled in the art that other leg designs can be employed (e.g. S shaped or C shaped structures) which provide the same function in supporting the ring structure. Additionally these legs may be attached either internally or externally to outer rim 7 of the ring structure.
For devices such as these, the radial and tangential stiffness of the legs should be significantly lower than that of the ring itself so that the modal vibration is dominated by the ring structure. The radial stiffness is largely determined by the length of the arcuate segment 9′″ of the leg. The straight segments 9′ and 9″ of the leg dominate the tangential stiffness. The overall length of the leg structure largely determines the out of plane stiffness. Maintaining the ring to leg compliance ratio, particularly for the radial stiffness, for this design of leg becomes increasingly difficult as the arc angle of the leg structure is restricted by the proximity of the adjacent legs. This requirement places onerous restrictions on the mechanical design of the support legs and necessitates the use of leg structures which are thin (in the plane of the ring) in comparison to the ring rim. This reduced dimension renders these structures more susceptible to the effects of dimensional tolerancing in the production processes of the mechanical structure. This will result in variation in the mass and stiffness of these supporting leg elements which will disturb the symmetry of the mode dynamics and hence induce frequency splitting of the response modes.
The structures described in the prior art may be fabricated in a variety of materials using a number of processes. Where such devices are fabricated from metal these may be conveniently machined to high precision using wire erosion techniques to achieve the accurate dimensional tolerancing required. This process involves sequentially machining away material around the edges of each leg and the ring structure. The machining time, and hence production cost, increases in proportion to the number of legs. The number of legs hitherto thought to be required increases rapidly with mode order. Minimising the number of legs is therefore highly desirable, particularly for designs employing higher order modes. Similar considerations apply to structures fabricated from other materials using alternative processes.
It would be desirable to be able to design planar ring structures for use in two-axis rate sensor devices which provide a large fixed frequency split between the cos Nθ carrier mode and its complementary sin Nθ mode thus fixing its orientation on the ring structure. This should be achieved whilst maintaining the dynamic symmetry of the sin(N±1)θ/cos(N±1)θ response mode pair such that their frequencies are matched. It would be advantageous to use a reduced number of support leg structures.